Systems of Equations (Substitution)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is substitution in the context of systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you determine if a system of equations has one solution?

Back

If the graphs of the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinite solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8B

Front

Solve the system using substitution: y = 8, y = -4x + 4.

Back

(-1, 8)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system using substitution: x = 6, y = 2x - 3.

Back

(6, 9)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system using substitution: 2y + x = -15, x = 3y.

Back

(-9, -3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6